Prasanta Chandra Mahalanobis (June 29, 1893–June 28, 1972) was an Indian scientist and applied statistician. He is best known for the Mahalanobis distance, a statistical measure. He did pioneering work on anthropometric variation in India. He founded the Indian Statistical Institute, and contributed to large scale sample surveys.
Inspired by Biometrika and mentored by Acharya Brajendra Nath Seal he started his statistical work. Initially he worked on analyzing university exam results, anthropometric measurements on Anglo-Indians of Calcutta and some metrological problems. He also worked as a meteorologist for some time. In 1924, when he was working on the probable error of results of agricultural experiments, he met Ronald Fisher, with whom he established a life-long friendship. He also worked on schemes to prevent floods.
His most important contributions are related to large scale sample surveys. He introduced the concept of pilot surveys and advocated the usefulness of sampling methods. His name is also associated with the scale free multivariate distance measure, the Mahalanobis distance. He founded the Indian Statistical Institute on 17 December, 1931.
In later life, he contributed prominently to newly independent India's five-year plans starting from the second. His variant of Wassily Leontief's neo-Marxist Input-output model, the Mahalanobis model, was employed in the Second Five Year Plan, which worked towards the rapid industrialization of India and with other colleagues at his institute, he played a key role in the development of a statistical infrastructure.
He was awarded the Weldon Medal from Oxford University in1944, Fellow of the Royal Society, in 1945, Honorary President, International Statistical Institute in1957 and Padma Vibhushan in 1968.
The government of India has decided to celebrate his birthday, 29 June, as National Statistical Day.
Courtesy:Internet
Sunday, December 16, 2007
Lalla
Lalla (720-790) was an Indian astronomer and mathematician who followed the tradition of Aryabhata I. Lalla's most famous work was entitled Shishyadhividdhidatantra.
This major treatise was in two volumes.
First volume: On the computation of the positions of the planets, was in thirteen chapters and covered topics such as: mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; lunar eclipses; solar eclipses; syzygies; risings and settings; the shadow of the moon; the moon's crescent; conjunctions of the planets with each other; conjunctions of the planets with the fixed stars; the patas of the moon and sun, and a final chapter in the first volume which forms a conclusion.
Second volume: On the sphere. In this volume Lalla examined topics such as: graphical representation; the celestial sphere; the principle of mean motion; the terrestrial sphere; motions and stations of the planets; geography; erroneous knowledge; instruments; and finally selected problems.
Lalla also wrote a commentary on Khandakhadyaka, a work of Brahmagupta. Lalla's commentary has not survived but there is another work on astrology by Lalla which has survived, namely the Jyotisaratnakosa. This was a very popular work which was the main one on the subject in India for around 300 years.
Courtesy:Internet
This major treatise was in two volumes.
First volume: On the computation of the positions of the planets, was in thirteen chapters and covered topics such as: mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; lunar eclipses; solar eclipses; syzygies; risings and settings; the shadow of the moon; the moon's crescent; conjunctions of the planets with each other; conjunctions of the planets with the fixed stars; the patas of the moon and sun, and a final chapter in the first volume which forms a conclusion.
Second volume: On the sphere. In this volume Lalla examined topics such as: graphical representation; the celestial sphere; the principle of mean motion; the terrestrial sphere; motions and stations of the planets; geography; erroneous knowledge; instruments; and finally selected problems.
Lalla also wrote a commentary on Khandakhadyaka, a work of Brahmagupta. Lalla's commentary has not survived but there is another work on astrology by Lalla which has survived, namely the Jyotisaratnakosa. This was a very popular work which was the main one on the subject in India for around 300 years.
Courtesy:Internet
Pandita Jagannatha Samrat
Pandita Jagannatha Samrat (1652-1744) was an Indian astronomer and mathematician in the court of Jai Singh II of Amber. He learned Arabic and Persian in order to study Islamic astronomy. His works include Rekhaganita, a translation of Euclid's Elements from Arabic; Siddhantasarakaustubha, a translation of the Almagest from Arabic; and two works on astronomical instruments such as the astrolabe, Siddhanta-samrat and Yantraprakara, which also record astronomical observations made by Jagannatha.
Courtesy:Internet
Courtesy:Internet
Saturday, December 15, 2007
Kamalakara
Kamalakara (1616-1700) born in Benaras, india, was an Indian astronomer and mathematician who came from a family of famous astronomers. Kamalakara's father was Nrsimha who was born in 1586. Two of Kamalakara's three brothers were also famous astronomer/ mathematicians, these being Divakara, who was the eldest of the brothers born in 1606, and Ranganatha who was younger than Kamalakara.
Kamalakara combined traditional Indian astronomy with Aristotelian physics and Ptolemaic astronomy as presented by Islamic scientists (especially Ulugh Beg). Following his family's tradition he wrote a commentary, Manorama, on Ganesa's Grahalaghava and, like his father, Nrsimha, another commentary on the Suryasiddhanta, called the Vasanabhasya.
Kamalakara's most famous work, the Siddhanta-tattva-viveka in 1658. The Siddhanta-tattva-viveka is a Sanskrit text and in it Kamalakara makes frequent use of the place-value number system with Sanskrit numerals.
Courtesy:Internet
Kamalakara combined traditional Indian astronomy with Aristotelian physics and Ptolemaic astronomy as presented by Islamic scientists (especially Ulugh Beg). Following his family's tradition he wrote a commentary, Manorama, on Ganesa's Grahalaghava and, like his father, Nrsimha, another commentary on the Suryasiddhanta, called the Vasanabhasya.
Kamalakara's most famous work, the Siddhanta-tattva-viveka in 1658. The Siddhanta-tattva-viveka is a Sanskrit text and in it Kamalakara makes frequent use of the place-value number system with Sanskrit numerals.
Courtesy:Internet
Munishvara
Munishvara (17th century) Indian mathematician, presented accurate sine tables.
Courtesy : Internet
Courtesy : Internet
Achyuta Pisharati
Achyuta Pisharati (1550–1621) was a renowned Sanskrit grammarian, astrologer and mathematician of his time. He was a student of Jyestadeva and a member of Madhava of Sangamagrama's Kerala school. He is remembered mainy for his part in the composition of his student Melpathur Narayana Bhattathiri's devotional poem, Narayaneeyam.
He discovered the technique of 'the reduction of the ecliptic'. He authored Sphuta-nirnaya , Raasi-gola-sphuta-neeti (raasi meaning zodiac, gola meaning sphere and neeti roughly meaning rule), Karanottama (1593) and a four- chapter treastise Uparagakriyakrama on lunar and solar eclipses.
Courtesy:Internet
He discovered the technique of 'the reduction of the ecliptic'. He authored Sphuta-nirnaya , Raasi-gola-sphuta-neeti (raasi meaning zodiac, gola meaning sphere and neeti roughly meaning rule), Karanottama (1593) and a four- chapter treastise Uparagakriyakrama on lunar and solar eclipses.
Courtesy:Internet
Jyesthadeva
Jyesthadeva (1500-1575) lived on the southwest coast of India in the district of Kerala. He belonged to the Kerala school of mathematics built on the work of Madhava, Nilakantha Somayaji, Paramesvara and others. Jyesthadeva wrote a famous text Yuktibhasa which he wrote in Malayalam, the regional language of Kerala. The work contains proofs of the theorems and gives derivations of the rules it contains. It is one of the main astronomical and mathematical texts produced by the Kerala school. The work was based mainly on the Tantrasamgraha of Nilakantha.
The Yuktibhasa is a major treatise, half on astronomy and half on mathematics, written in 1501. The Yuktibhasa is very important in terms of the mathematics Jyesthadeva presents. In particular he presents results discovered by Madhava and the treatise is an important source of the remarkable mathematical theorems which Madhava discovered. Written in about 1550, Jyesthadeva's commentary contained proofs of the earlier results by Madhava and Nilakantha which these earlier authors did not give.
Yuktibhasa describing Madhava's series, but remember that even this passage by Jyesthadeva was written more than 100 years before James Gregory rediscovered this series expansion. Other mathematical results presented by Jyesthadeva include topics studied by earlier Indian mathematicians such as integer solutions of systems of first degree equation solved by the kuttaka method, and rules of finding the sines and the cosines of the sum and difference of two angles.
Not only does the mathematics anticipate work by European mathematicians a century later, but the planetary theory presented by Jyesthadeva is similar to that adopted by Tycho Brahe.
Courtesy:Internet
The Yuktibhasa is a major treatise, half on astronomy and half on mathematics, written in 1501. The Yuktibhasa is very important in terms of the mathematics Jyesthadeva presents. In particular he presents results discovered by Madhava and the treatise is an important source of the remarkable mathematical theorems which Madhava discovered. Written in about 1550, Jyesthadeva's commentary contained proofs of the earlier results by Madhava and Nilakantha which these earlier authors did not give.
Yuktibhasa describing Madhava's series, but remember that even this passage by Jyesthadeva was written more than 100 years before James Gregory rediscovered this series expansion. Other mathematical results presented by Jyesthadeva include topics studied by earlier Indian mathematicians such as integer solutions of systems of first degree equation solved by the kuttaka method, and rules of finding the sines and the cosines of the sum and difference of two angles.
Not only does the mathematics anticipate work by European mathematicians a century later, but the planetary theory presented by Jyesthadeva is similar to that adopted by Tycho Brahe.
Courtesy:Internet
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